Topological obstructions to nonnegative curvature
Igor Belegradek, Vitali Kapovitch
Abstract
We find new obstructions to the existence of complete Riemannian metric of nonnegative sectional curvature on manifolds with infinite fundamental groups. In particular, we construct many examples of vector bundles whose total spaces admit no nonnegatively curved metric.
Create a lesson
Related papers
The Bernstein problem in higher dimensional Heisenberg groups
Gianmarco Giovannardi, Simone Verzellesi
A Lean Formalization of the Hamilton--Perelman Proof of Thurston's Geometrization Conjecture
Yuan Liao, Ziyang Qin, Jui-Hui Chung et al.
A counterexample to Nirenberg's conjecture on closed asymptotic curves
Harrison Banks, Mohammad Ghomi, Hongda Qiu et al.
Topping's conjecture for solutions of harmonic map flow with isolated bubbles
Melanie Rupflin, Alex Waldron, Sebastian Woodward
The Renormalized Area--Willmore Relation
Alvaro Pampano, Aaron J. Tyrrell
Compact lcK manifolds with Gauduchon parallel vector fields
Andrei Moroianu, Giacomo Perri